Orders for espresso-based beverages are collected by the waitstaff and assigned to one of the three baristas, using a dedicated order queue for each barista, as shown in Figure 2. Orders are placed in each of the three baristas' queues at the rate of 39/hour in what may be assumed to be Poisson processes.

Each barista is assigned and operates a Victoria Arduino Venus bar, and independently processes orders in hir queue. For the purposes of this analysis, assume that each barista/Victoria Arduino Venus bar processes espresso-based beverage orders at the rate of 43/hour. This means that each beverage takes 1.395 minutes on average to make. The three baristas are all relatively new to the job, and the standard deviation of the time they each take to make an espresso-based beverage is 1.4 minutes. A recent TripAdvisor survey suggests that baristas are making many mistakes with the orders (which they then have to redo). Advanced barista training that would reduce the standard deviation of the time of barista order execution by 25% (at a cost of x), by 40% (at a cost of 2x), by 65% (at a cost of 4x) and by 82% (at a cost of 7x), is available. These cost multiples are a rough estimate from a consultant; the value of x in the market is currently being researched using an RFP.

How to improve the current operation? Should ACG consider substituting one or two of the semi-automatic Victoria Arduinos Venus bars with fully automated alternatives?

As a function of the number of baristas using the current order queue design. Tip: use the M/M/1 model and/or Kingman's formula.

If the orders are pooled in a single queue that all the baristas serve. Tip: use the M/M/k formula.

1. Calculate the average time waiting in line and the average time spent in the system for each situation. (current, pooling, training, pooling & training, automation, pooling & automation)